Question: Simplify. Rewrite the expression in the form $a^n$. $\dfrac{a \cdot a \cdot a \cdot a \cdot a \cdot a}{a}=$
Solution: $\dfrac{a \cdot a \cdot a \cdot a \cdot a \cdot a}{a}= \dfrac{a^6} {a^1} $ $\begin{aligned} \dfrac{a^{6}}{a^1}&=\dfrac{\overbrace{\cancel a\cdot a\cdot a\cdot a\cdot a\cdot a}^\text{6 times}}{\underbrace{\cancel a}_\text{1 time}} \\\\\\ &=\underbrace{a\cdot a\cdot a\cdot a\cdot a}_\text{5 times} \\\\ \end{aligned}$ When powers have the same base $\dfrac{x^m}{x^n}=x^{m-n}$. $\begin{aligned} \dfrac{a^{6}}{a}&=\dfrac{a^{6}}{a^1} \\\\ &=a^{6-1} \\\\ &=a^5 \end{aligned}$ $\dfrac{a \cdot a \cdot a \cdot a \cdot a \cdot a}{a}=a^5$